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Record W2904782129 · doi:10.22215/etd/2015-10822

Efficient Density Estimation using Fejer-Type Kernel Functions

2015· dissertation· en· W2904782129 on OpenAlexaff
Olga Kosta

Bibliographic record

Venuenot available
Typedissertation
Languageen
FieldMathematics
TopicStatistical Methods and Inference
Canadian institutionsCarleton University
Fundersnot available
KeywordsEstimatorMathematicsMinimaxKernel density estimationSmoothingKernel smootherApplied mathematicsKernel (algebra)Variable kernel density estimationMultivariate kernel density estimationBandwidth (computing)Minimax estimatorFourier seriesFourier transformMathematical optimizationKernel methodStatisticsComputer scienceDiscrete mathematicsRadial basis function kernelMathematical analysisMinimum-variance unbiased estimatorSupport vector machineArtificial intelligence

Abstract

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The problem of estimating an unknown probability density function (pdf) is of fundamental importance in statistics and required for many statistical applications. In recent years, efficient nonparametric estimation has had greater focus on the problem of nonparametric regression, while the more challenging problem of density estimation has been given much less attention. In this thesis, we consider a class of kernel-type density estimators with Fejr-type kernels and theoretical smoothing parameters h n = (2 n )/ log n, where the parameter > 0 describes the class of underlying pdfs and 0 n < 1. In theory, the estimator under consideration dominates in L p , 1 p < , all other known estimators from the literature in the locally asymptotic minimax (LAM) sense. We demonstrate via simulations that the estimator in question is good by comparing its performance to other fixed kernel estimators. The kernel-type estimator is also studied under empirical bandwidth selection methods such as the common cross-validation and the less-known method based on the Fourier analysis of kernel density estimators. The common L 2 -risk is used to assess the quality of estimation. The estimator of interest is then tried to real financial data for a risk measure that is widely used in many applications. The simulation results testify that, for a good choice of , the theoretical estimator under study provides very good finite sample performance compared to the other kernel estimators. The study also suggests that the bandwidth obtained by using the Fourier analysis techniques performs better than the one from cross-validation in most settings.

Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.

How this classification was reachedexpand

Full frame distilled prediction

Teacher imitation

Not calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.

metaresearch head score (Codex)0.000
metaresearch head score (Gemma)0.004
Version: codex-gemma-dda1882f352aValidation status: machine_predicted_unvalidated
Candidate categoriesnone
Consensus categoriesnone
DomainCandidate signal: none · Consensus signal: none
Study designCandidate signal: Theoretical or conceptual · Consensus signal: none
GenreCandidate signal: Methods · Consensus signal: Methods
Teacher disagreement score0.516
Threshold uncertainty score0.808

Codex and Gemma teacher scores by category

CategoryCodexGemma
Metaresearch0.0000.004
Meta-epidemiology (narrow)0.0000.000
Meta-epidemiology (broad)0.0000.000
Bibliometrics0.0000.000
Science and technology studies0.0000.000
Scholarly communication0.0000.000
Open science0.0000.000
Research integrity0.0000.000
Insufficient payload (model declined to judge)0.0010.000

Machine scores (provisional)

The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.

Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.

Opus teacher head0.171
GPT teacher head0.441
Teacher spread0.271 · how far apart the two teachers sit on this one work
Validation statusscore_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from it

Classification

machine, unvalidated

Machine predicted; a candidate call from one teacher head, not a consensus.

The models applied no category: nothing in the taxonomy fit this work.
Study designTheoretical or conceptual
Domainnot available
GenreMethods

How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".

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Citations1
Published2015
Admission routes1
Has abstractyes

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